Two migrants have drowned and 30 more are missing after their boats capsized in the Aegean sea, Greece's coastguard said on Monday.

More than 60 migrants of unknown nationality had attempted to cross the sea from neighbouring Turkey when their two dinghies capsized near the Greek island of Samos, the coastguard said.

It has so far picked up 36 survivors and two dead, and the operation is ongoing.

"Two drowned bodies were found and 36 migrants have been rescued ... About 30 are missing," an official told Reuters.

Authorities said they did not yet know the nationality of the migrants. Two air force helicopters, assisted by two coastguard vessels, one navy warship and a cruise liner were searching for the missing, the coast guard official said.

Greece, Italy and Malta have repeatedly pressed European Union partners to do more to help them handle the large numbers of migrants.

Greece is one of the main ports of entry into the European Union for people fleeing war-torn and impoverished countries in Africa, the Middle East and the Indian subcontinent.

People traffickers are using Greece's Aegean islands as a preferred route into Europe following a tightening of migration controls along its land border with Turkey.